Discrete methods of the energy equations in the pseudo-potential lattice Boltzmann model based simulations

Pseudo-potential lattice Boltzmann (LB) Methods have been widely applied in the gas-liquid multiphase flow and heat transfer simulations such as the bubble growth in the boiling process. Various formats of energy equations and discrete models are deduced to solve the heat transition in the simulations. However, the accuracy of these models has rarely been discussed. In this paper, four common LB thermal models are analyzed and numerically compared with the finite difference method by simulating the phenomena of single-phase natural convection and the one-dimensional heat transfer across the vapor-liquid interface. Simulation results show that all these LB thermal models lead to unwanted errors compared with the benchmark simulation results, while, with the proper discrete scheme, the finite difference method provides results with much better accuracy. With the presented finite difference model, we further compared the energy conservation of the energy equations in the phase change simulation. It is found that the accuracy and the thermodynamic consistency of the temperature-based energy equation is better than the internal-energy-based energy equation.